POJ 3709

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <cstring>
#define N 500050
#define LL __int64
using namespace std;

LL sum[N],dp[N]; int q[N];
int a[N];
int head,tail;

LL getUp(int j,int k){
	return dp[j]-sum[j]+a[j+1]*j-(dp[k]-sum[k]+a[k+1]*k);
}

LL getDown(int j,int k){
	return a[j+1]-a[k+1];
}

int main(){
	int n,T,tmp,k;
	scanf("%d",&T);
	while(T--){
		scanf("%d%d",&n,&k);
		sum[0]=0;
		for(int i=1;i<=n;i++){
			scanf("%d",&a[i]);
			sum[i]=sum[i-1]+(LL)a[i];
	//		cout<<sum[i]<<‘ ‘;
			dp[i]=0;
		}
//		cout<<endl;
		head=tail=0;
		int i;
		for(i=1;i<=2*k&&i<=n;i++){
			dp[i]=sum[i]-sum[0]-((LL)a[1])*((LL)i);
	//		cout<<dp[i]<<‘ ‘;
		}
	//	cout<<endl;
		i--;
		if(i==2*k){
			dp[i]=min(dp[i],dp[k]+sum[i]-sum[k]-(LL)a[k+1]*(i-k));
			q[tail++]=k;
			q[tail++]=k+1;
			for(++i;i<=n;i++){
				dp[i]=sum[i]-sum[0]-((LL)a[1])*((LL)i);
			//	cout<<dp[i]<<endl;
				while(head<tail-1&&getUp(q[head+1],q[head])<=((LL)i)*getDown(q[head+1],q[head]))
				head++;
			//	cout<<q[head]<<endl;
				dp[i]=min(dp[i],dp[q[head]]+sum[i]-sum[q[head]]-((LL)a[q[head]+1]*(LL)(i-q[head])));
				while(head<tail-1&&getUp(i-k+1,q[tail-1])*getDown(q[tail-1],q[tail-2])<=getUp(q[tail-1],q[tail-2])*getDown(i-k+1,q[tail-1]))
				tail--;
				q[tail++]=i-k+1;
			}
		}
		printf("%I64d\n",dp[n]);
	}
	return 0;
}